Afghan President Hamid Karzai is meeting US President George W Bush for talks at Camp David near Washington.
The talks are billed as a "strategy session" on fighting the Taleban
They are expected to discuss the fight against the Taleban and al-Qaeda and the growing number of civilians killed in coalition military operations.
The drug trade, economic development and the fate of 21 remaining South Korean hostages held by the Taleban are also likely to be high on the agenda.
Two South Koreans from the group have already been killed by their captors.
The two days of talks between the Afghan and US leaders are being billed as a "strategy session" on combating the Taleban insurgency.
Mr Bush is also expected to urge Mr Karzai to assert his government's authority throughout the country and root out corruption.
This year the US is giving Afghanistan $10bn, targeted at building up the country's own security forces.
Mr Karzai is concerned about the number of civilian casualties
Mr Bush wants to see results, says the BBC's Jonathan Beale in Washington.
Mr Karzai is concerned about the growing number of civilians killed in military operations.
He also wants the US to press its ally, Pakistan, to do more to tackle fighters crossing the border into Afghanistan.
But our correspondent says the US is just as worried about the influence of neighbouring Iran, accusing Tehran of supplying weapons to the Taleban.
Mr Karzai appeared to rebut such claims in an interview with CNN taped on Saturday in Kabul, calling Iran "a helper and a solution".
"Iran has been a supporter of Afghanistan, in the peace process that we have and the fight against terror, and the fight against narcotics in Afghanistan," he said.
Mr Karzai also said he would do everything he could to have the 21 South Korean hostages released short of "anything that will encourage hostage-taking, that will encourage terrorism".
Two of the hostages are reported to be seriously ill.
The head of a private Afghan clinic, Mohammad Hashim Wahaj, said more than $1,200 worth of antibiotics, pain killers, vitamins and heart pills had been left in an area of desert in Ghazni province, where the hostages are being held, specified by the militants.
"This is a big achievement. Among the Koreans are doctors who know how to use these medicines," he said, quoted by Reuters news agency.
"It was a big risk, but we had to take the risk because it is a humanitarian issue."
Mr Wahaj told reporters the Taleban had expressed readiness to swap the two sick hostages for two imprisoned Taleban fighters.
Earlier, the province's governor said Pakistani Taleban and military intelligence officers had taken charge of the hostage situation from local Afghan Taleban, and were trying to show that the Afghan government was weak.
Four Afghans and a German are also being held hostage by another group of Taleban.